The present invention relates in general to the field of electrical impedance tomography and in particular to new and useful methods for the selection of the current pattern or patterns best suited for use in implementing certain impedance tomography systems when specific goals for the system are known. While the apparatus and methods shown here are intended for use in the medical area for distinguishing internal structures of the human body non-invasively, many other applications exist for systems with these capabilities in areas such as flaw detection, geology, food and other material processing, etc.
An apparatus for practicing electric impedance tomography is disclosed in an article by the coinventors of the present invention, entitled "An Electric Current Tomograph", IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, Vol. 35 No. 10, October, 1988. A process and apparatus for utilizing a similar array of electrodes in electrical impedance tomography is disclosed in U.S. Pat. No. 4,920,490, granted to one of the Coinventors of the present invention. U.S. Pat. No. 4,920,490 is incorporated here by reference, and discloses a means to determine the shape of a single current pattern that best distinguishes the presence of a region of any conductivity inside a body different from a known uniform conductivity or of any two conductivity distributions from each other.
The parent U.S. patent application Ser. No. 07/734,591 to the present case, teaches a method for utilizing the same apparatus to determine the values, point by point, of an unknown distribution of conductivities present inside a body by finding the complete set of optimal current patterns required to best distinguish the unknown distribution from an arbitrary guessed distribution and then from successively closer approximations to the actual distribution. This iterative process requires a method for calculating the voltage to be expected at each electrode for each conductivity distribution and each set of current patterns used. This process may be used to find a conductivity distribution that may then be presented to a user in the form of a cross-sectional image, or conductivity map.
All impedance measurements have two attributes, a real, or in-phase component related to energy loss, which results in resistive information and the imaginary, or quadrature component which result in reactive information related to energy storage. The magnitude of the specific impedance of an element of a body is given by the square root of the sum of the squares of the resistivity and reactivity of that element where the resistivity and reactivity are considered series elements.
In a similar way the reciprocal of the specific impedance magnitude, the admittivity magnitude, is the square root of the sum of the squares of the conductivity and susceptivity, which are considered as elements in parallel. The susceptivity, is the angular frequency times the permittivity. Since the permittivity is more constant with frequency than other reactive terms in most materials, and is so easily related to them, it is the quantity of choice, along with conductivity and admittivity, the phasor sum of the conductivity and susceptivity. Conductivity and susceptivity may easily be calculated from resistivity and reactivity values.
When using an impedance imaging system, an apparatus for finding information about the interior of a body using measurements made on its surface, one might have any of several goals. If one were only concerned with whether the area being examined was uniform and homogeneous or whether it contained some inhomogeneity, such as an internal crack in a metal sample, and if detecting the presence of the crack were the only goal, then one need apply only a single spatial pattern of currents to the electrodes. The question of what should be its shape was answered by Isaacson in U.S. Pat. No. 4,920,490.
In many applications of impedance imaging it is not sufficient to determine that some region has an impedance distribution different from that expected. Instead, one would like to produce a fully reconstructed image of the admittance pattern in the region of interest. The number of picture elements desired usually exceeds the number of electrodes used, so it is necessary to apply not one, but many independent spatial current patterns to the electrodes. The number of independent patterns is limited to less than the number of electrodes, so that, for instance, in a 32 electrodes system 31 patterns may be sequentially applied, resulting in 31.times.32 or 992 separate voltage measurements for real, an equal number for reactive, and a maximum of 496 picture elements.
The user of the system nearly always wishes for the best possible images. These require many electrodes and the best possible current stability and measurement precision. When used with humans, there are limits to the maximum currents or powers that may be employed. Improvement in effective signal-to-noise ratio of the voltmeters can be produced by the use of current patterns whose shapes force more current to flow through regions of the sample of special interest. Unfortunately, adaptive methods that produce optimal current patterns for improved images require considerable time for both calculations and many repetitive data measurements. Whenever the fastest possible acquisition and processing of image data is needed for cylindrical geometry, it is most expedient to use the full set of sinusoidal current patterns, of increasing spatial frequency, which we designate the canonical patterns. Along with these, an approximate solution for the distribution of admittivities in the sample based on the canonical current patterns applied and the voltages measured has been developed. It is based on the first step of Newtons method, and designated is NOSER.